Barenaked Ladies and Ben Folds Five are currently roaming the country on a jaunt called “Last Summer on Earth” tour, which comes to the Bank of America Pavilion on Tuesday. Do they know something we don’t?

“We actually started the tour last year,” says BNL frontman Ed Robertson, noting that 2012 was the year the Mayan calendar predicted the end of the world. “This year, we’re just hedging our bets. Maybe the Mayans forgot to carry the one or something and maybe it ends this year. We’re going to keep doing the ‘Last Summer on Earth’ tour until the world ends. And then we’ll say, ‘See, told you so!’ ’’

Both groups are promoting new releases, the excellent “Grinning Streak” for Canada’s BNL and the live album from the reunited-in-2011 piano pop trio BFF. The longtime mutual admirers are excited to be out together.

“We’re bands that grew up and cut our teeth together,” says Robertson of BFF and Guster. (The Boston-spawned group is appearing on almost all the other dates on the “Last Summer” tour but skipped Boston in favor of opening for Dispatch last month at the Comcast Center.)

We recently chatted with Robertson and Folds from a Columbus, Ohio, tour stop, posing questions both serious and silly.

Q. You both have blatant untruths in your name. Which is worse, that Ben Folds Five is a trio or the dearth of nude females in BNL?

ROBERTSON: What’s funny is my high school band was called Three Guys From Barrie and there were five of us. And none of us were from Barrie so it was doubly misleading.

FOLDS: They’re both pretty bad names. If you’ve never heard of either one of our bands they could sort of exist on some lounge marquee at a Four Seasons somewhere and people would say “God, what a [expletive] name.” I think once you make records, there’s an association with it and then it’s good. I like that both names are playful because what else are you going to do?

Q. In a “Battle of the Network Stars”-type competition, who is the victor among your bands?

ROBERTSON: I would have to say Guster would be our strongest competition — Brian Rosenworcel, Adam Gardner, Luke Reynolds — there are three physical specimens to be reckoned with. I’ve totally ruled Ben Folds Five out, they’re not even in the competition. I think it’s definitely between Guster and Barenaked Ladies, and ultimately we get inside their heads and we win.

FOLDS: We don’t have enough people for that. [BFF drummer] Darren [Jessee] doesn’t really like to move. [Bassist] Robert [Sledge] is pretty strong. I just don’t weigh enough. On tug-of-war they’d just yank my ass across the line.

ROBERTSON: Hey, what are you trying to say, Ben?

Q. That you’re strong and powerful?

ROBERTSON: No he’s trying to say we weigh a lot. [Laughs.]

FOLDS: You’re tall and built.

ROBERTSON: It’s true we are the tallest band in rock ’n’ roll. We have three guys over 6 feet.

Q. How about in a more brain-teaser-like competition such as Scrabble?

ROBERTSON: That’s tough. I think the last men at the board would be myself, [Guster frontman] Ryan Miller, and Ben. But among us I’m probably the only one who has read Stefan Fatsis’s book about Scrabble and also narrated a documentary on Scrabble, so I may have a competitive edge.

FOLDS: I’m not really very good at Scrabble. I think Robert probably would be. If I had the help of my girlfriend I could kick all of y’all’s asses.

Q. Are there songs in each other’s catalogs you wish you’d written?

FOLDS: “Lying in bed just like Brian Wilson did,” I think that’s a neat lyric [from “Brian Wilson.”] In fact, I guess I thought I’d wished I’d written enough to where I have a similar sounding cadence in a line on a song called “Rockin’ the Suburbs,” “just like Jon Bon Jovi did.” There’s something funny about putting “did” at the end of the sentence, it’s real conversational. It’s also got a melancholy feel to the lyric while the song sounds happy and I like that.

ROBERTSON: I love “Army.” I try to catch it every night. It’s such a great song, it’s a such a great story. I will often make a mixtape-type playlist for somebody to describe the kind of music that I like and that’s always one that I put on there. I think the lyrics come across totally conversational, nothing seems forced.

Q. The a cappella competition “The Sing-Off,” on which Ben serves as a judge, is returning to NBC this winter. Ed will you pledge right now to bring BNL on the show for a sing-off?

ROBERTSON: We’ve been talking about organizing a freestyle rap battle between me, Ben, and Ryan. I think it would be pretty killer. [Ben laughs.]

FOLDS: I’ll do that. I think the Barenaked Ladies could kill on an a cappella show.

ROBERTSON: We’re actually working up an a cappella version of “Army” right now.

FOLDS: It’s a shoo-in, they’re on.

Q. Ben when you toured with Guster and Rufus Wainwright, you and Rufus did a great version of “Careless Whisper” by Wham! Will you all be doing any onstage collaborations like that?

ROBERTSON: You guys do “Careless Whisper”? Dude, we do “Careless Whisper”! I think we might’ve done “Careless Whisper” with Guster back in the day.

FOLDS: When you say back in the day, how far back?

ROBERTSON: Oh God, probably late ’60s, early ’70s.

FOLDS:
OK, well that’s definitely after ours because ours was in the ’30s and it was only a wire recording.

ROBERTSON: You know what, we recorded it with the Guster guys and now I’m remembering it originally came out on player piano rolls. It was originally arranged for hurdy-gurdy.

FOLDS: Yeah, well it wasn’t called “Careless Whisper” back when we did it. It was called “Unga Unga Un” and it was some rocks smashed together.

Q. Now that you’ve found this common ground, is it possible that you’ll perform together?

ROBERTSON: Ben has been out to rock a little piano with us and he has an open invite, and I hope he will take advantage of it more.

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